Nonlinear sampling type operators: approximation properties and regular methods of summability
Nonlinear sampling type operators: approximation properties and regular methods of summability
The authors consider a general class of nonlinear integral operators of the form \[ (T_\omega f)(s)= \int_HK_\omega \bigl(s-h_\omega (t), f(h_\omega(t) \bigr)d \mu_H(t),\tag{1} \] where \(\omega>0\), \(s\in G\), \(G\) and \(H\) are topological groups, \(\{h_\omega\}\) is a family of homeomorphisms, \(\{K_\omega\}_{\omega >0}\) is a family of kernels satisfying suitable assumptions, \(\mu_H\) is the Haar measure on \(H\) and \(f\) belongs to a functional space. For such operators results concerning the uniform and modular approximation are presented. Moreover, the connections between uniform or modular approximation properties with the problem of regular methods of summability for the operators (1) are investigated.
- University of Perugia Italy
Linear operator approximation theory, order of approximation, nonlinear integral operators, Linear operators on function spaces (general), Approximation by operators (in particular, by integral operators), methods of summability, Rate of convergence, degree of approximation, Order of approximation; nonlinear integral operators; uniform convergence; methods of summability, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Linear operator approximation theory, order of approximation, nonlinear integral operators, Linear operators on function spaces (general), Approximation by operators (in particular, by integral operators), methods of summability, Rate of convergence, degree of approximation, Order of approximation; nonlinear integral operators; uniform convergence; methods of summability, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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